The transformation of raw materials into product in a chemical processing plant requires the use of energy. The energy may be supplied from a utility source independent of the chemical processing plant and is usually dependent upon a contractual arrangement with the utility company. In an air separation and liquefication process plant the cost of raw material is for all practical purposes equal to the cost of electrical energy. As such, product cost will vary with the cost of electrical energy which, in turn, is dependent upon product production rate over a given time horizon and the contractual terms of purchase. Minimizing the quantity of electrical energy used to meet a desired demand for output product in a given time period will minimize production costs only if the cost of energy is a simple function of the quantity of energy used. Although it is product demand which determines how much energy is used the cost of energy is dependent upon when in time the energy is purchased and the amount of energy purchased, i.e., consumed, in that time period. In general, the cost becomes a function of how much energy is used, when it is used, and how it is used. A typical contractual feature of a utility contract is to charge the site both for total energy used and the maximum use rate taken over some contract billing period. The latter feature represents a fixed charge based on the maximum energy use rate. Under many contracts, the unit cost of energy varies discontinuously by time of day. For such contracts, there is an incentive to produce at higher levels when the energy is less expensive and reduce energy use during the times when the energy is more expensive. It is, however, necessary to account for the cost of the availability of energy independent of use. Moreover, the level of output production from an air separation plant should be held constant over any given time period in which the cost of energy is a constant unless other constraints such as the requirement to meet short term customer demands force it to be changed.
The production of a product can be limited to a single plant or it can be produced at a production site which consists of a number of interconnected plants producing common products which are combined to meet product demand. Each plant within a production site has capacity constraints, i.e., capacity limitations, and ranges defined by the physical limitations of the process equipment in the plant. The optimization of the production of a product from a production site relative to the cost of energy is independent of the distribution of the product from the production site and its optimization. Standard product allocation models exist to optimize the distribution of the products produced at the production site. A given product is produced within upper and lower limits of production rate depending upon plant equipment, the product, and the rates at which other products are made. The schedule for production of product from a production site must account for pipeline requirements and site production levels which is, in turn, dependent upon equipment constraints, ambient conditions and power availability.